(CNN) -- Some passengers on a diverted Aeromexico flight finally reached their destination in Seattle, Washington, on Wednesday after spending 16 hours in limbo.

The plane was scheduled to fly from Mexico City, Mexico, to Seattle on Tuesday, but was diverted to Portland, Oregon, because of thick fog, said Kara Simonds, a spokeswoman for Portland International Airport.

In Portland, the passengers were not allowed to exit the plane for four hours because the airport did not have enough customs agents to process them, according to CNN affiliate KING.

KING also reported several passengers became so angry that police boarded the plane and told them to stay there or be arrested.

Fire officials tried to calm down the outraged passengers by providing them with burgers from a local fast-food restaurant during their wait, Simonds said.

Passengers were then flown back to Mexico City after officials could not solve the issue with customs agents, Simonds said.

Seattle residents Mike and Karin Kuntz said they had a good vacation in Mexico, but it went downhill after they tried to get home.

"We had a wonderful time, everything went great. Then the flight home turned into a nightmare," Karin Kuntz told KING. "We just felt like we were hostages -- that we, as passengers, had no rights."

Karin Kuntz said she was concerned about the pilot's fatigue and the safety.

"Can he fly back? Is he logged in? How many hours does he have," she said. "No one seemed to be concerned about putting us back on that plane for all that time and that poor tired pilot."

The couple said they waited in the airport in Mexico City for 10 hours before getting a flight back to Seattle on Wednesday night.

It is unclear whether other passengers on the flight were able to get to their destination. Representatives from Aeromexico said they were investigating the situation and issued a statement apologizing for the inconvenience.

"We will seek an explanation about why the customs agents were not available to assist the plane and its passengers in Portland," the statement said. "We will also take appropriate steps to thank the passengers who were inconvenienced by this situation for their patience."

However, the ordeal did not end for the Kuntzes when they reached Seattle.

"They lost one of our bags," Mike Kuntz said.

It is unclear if other passengers on the flight were able to get to their destination. Representatives from Aeromexico said they were investigating the situation and planned to release a statement.